Fundamental solution of k-hyperbolic harmonic functions in odd spaces

30th International Colloquium on Group Theoretical Methods in Physics

Eriksson, Sirkka-Liisa^1 ; Orelma, Heikki^1

Department of Mathematics, Tampere University of Technology, P.O.Box 553, Tampere

FI-33101, Finland^1

关键词: Axially symmetric;    Fundamental solutions;    Half spaces;    Hyperbolic distances;    Laplace operator;    Laplace-Beltrami operator;    Poincare;    Riemannian metrics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012034/pdf
DOI  :  10.1088/1742-6596/597/1/012034

来源: IOP

【 摘 要 】

We study k-hyperbolic harmonic functions in the upper half space . The operator is the Laplace-Beltrami operator with respect to the Riemannian metric . In case k = n - 1 the Riemannian metric is the hyperbolic distance of Poincare upper half space. The proposed functions are connected to the axially symmetric potentials studied notably by Weinstein, Huber and Leutwiler. We present the fundamental solution in case n is even using the hyperbolic metric. The main tool is the transformation of k-hyperbolic harmonic functions to eigenfunctions of the hyperbolic Laplace operator.